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A304359
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Antidiagonal sums of the second quadrant of array A(k,m) = F_k(m), F_k(m) being the k-th Fibonacci polynomial evaluated at m.
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2
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0, 1, 1, 1, 1, 1, 0, 2, 1, -10, 39, -58, -166, 1611, -6311, 10083, 54195, -565257, 2727568, -6102368, -26464605, 394614352, -2515452801, 8797315672, 11441288836, -458369484247, 4097437715969, -21769011878335, 36715605929957, 703213495381553, -10042075731879152
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OFFSET
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0,8
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COMMENTS
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Equivalently, antidiagonal sums of the fourth quadrant of array A(k,m).
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LINKS
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FORMULA
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a(n) = Sum_{j=0..n} F_j(j-n).
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MAPLE
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F:= (n, k)-> (<<0|1>, <1|k>>^n)[1, 2]:
a:= n-> add(F(-j, n-j), j=0..n):
seq(a(n), n=0..30);
# second Maple program:
F:= proc(n, k) option remember;
`if`(n<2, n, k*F(n-1, k)+F(n-2, k))
end:
a:= n-> add(F(j, j-n), j=0..n):
seq(a(n), n=0..30);
# third Maple program:
a:= n-> add(combinat[fibonacci](j, j-n), j=0..n):
seq(a(n), n=0..30);
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MATHEMATICA
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a[n_] := Sum[Fibonacci[j, j - n], {j, 0, n}];
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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